1 Introduction

Since the beginning of the COVID-19 epidemic, policy makers in different countries have introduced different political action to contrast the contagion. The containment restrictions span from worldwide curfews, stay-at-home orders, shelter-in-place orders, shutdowns/lockdowns to softer measures and stay-at-home recommendations and including in addition the development of contact tracing strategies and specific testing policies. The pandemic has resulted in the largest amount of shutdowns/lockdowns worldwide at the same time in history.

The timing of the different interventions with respect to the spread of the contagion both at a global and intra-national level has been very different from country to country. This, in combination with demographical, economic, health-care related and area-specific factors, have resulted in different contagion patterns across the world.

Therefore, our goal is two-fold. The aim is to measure the effect of the different political actions by analysing and comparing types of actions from a global perspective and, at the same time, to benchmark the effect of the same action in an heterogeneous framework such as the Italian regional context.

different regions of Italy.

2 Data

The data used in this analysis refer to mainly two open datasets, i.e., the COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University for contagion data (Dong, Du, and Gardner (2020)) and Oxford COVID-19 Government Response Tracker (OxCGRT) for policies tracking (Thomas et al. (2020)).

3 Containment strategies and resembling patterns

4 Effect of policies from a global perspective

Some countries have underestimated the dangerousness of the Coronavirus disease 2019 (COVID-19) and the importance to apply the containment measures. The little concern of some countries regarding the COVID-19 infectious disease is due by many and different reason. Some countries decided to save the economy instead of people lives, i.e., it is a method to fight a war, in this case the pandemic war. For that, we want to analyze which coutries adopt the ``optimal’’ policy measures to contain the contagion of COVID-19. Thanks to the Thomas et al. (2020) data sets, we know which type of measures each goverment take and when. The indicators of government response considered are \(17\) in total, that can be resumed in indicators of lockdown/social distancing, contact tracing, movement restrictions, testing policy, public health measures, and governance and socio-economic measures.

Therefore, some variables as the number of hospital beds are considered from OECD in order to have some additional covariates that can be influence the variation in government responses to COVID-19.

We restrict the wide range of responses to COVID-19 from governments around the countries analyzed in Section 3, i.e., Korea, Singapore, Germany, Canada, Sweden, Greece, Portugal, Spain, United States of America, Irland, United Kingdom, Italy, Netherlands, Austria, Switzerland, Finland, Norway, Denmark, and France.

The daily number of active person is analyzed as measure of COVID-19 situation. Being a count variable, we decide to use a Negative Binomial Regression in order to correct also for the possible overdispersion. Therefore, the hierarchical struture induced by the nested structure of countries inside the clusters and by the repeated measures statement. For that, we think to use a generalized mixed model with family negative binomial. The countries information as well as the clusters and date information are used as random effects in our model.

So, the aim is to understand how the lockdown policies influences the contagions. We consider the aligned data respect to the first confirmed case, we have the following situation:

Also, we lag the number of active respect to \(14\) days, in order to consider the influences of the restrictions imposed at time \(t\) on number of active at time \(t+14\), in order to make a correct impact. The observations are aligned respect to the first confirmed case across the countries, in order to have observations directly comparable in a longitudinal point of view.

4.1 Exploratory Analysis

The set of covariates considered in this analysis can be divided into three main area:

  1. Longitudinal economic variables;

  2. Longitudinal health vystem variables;

  3. Fixed demographic/economic/health variables.

4.1.1 Economic Variables

Name Measurement Description
Income Support Ordinal Government income support to people that lose their jobs
Debt/contract relief for households Ordinal Government policies imposed to freeze financial obligations
Fiscal measures USD Economic fiscal stimuli
International support USD monetary value spending to other countries

We will combine these two first economic variables into one continous variables using the Polychoric Principal Component Analysis, in order to diminuish the number of covariates inside the model, having \(9\) ordinal policies lockdown covariates.

FALSE Converted non-numeric input to numeric

Therefore, the two economic variables in USD are examined and transformed in logarithmic scale in order to de-emphasizes very large values.

For further details about the definition of the economic variables, please see

4.1.2 Demographic/Fixed variables

4.1.3 Health variables

Name Measurement Description
Emergency Investment in healthcare USD Short-term spending on, e.g, hospitals, masks, etc
Investment in vaccines USD Announced public
spending on vaccine development 
FALSE Don't know how to automatically pick scale for object of type difftime. Defaulting to continuous.
FALSE `geom_smooth()` using method = 'loess' and formula 'y ~ x'
FALSE Don't know how to automatically pick scale for object of type difftime. Defaulting to continuous.
FALSE `geom_smooth()` using method = 'loess' and formula 'y ~ x'

pca.

4.2 Model

The data are observed for each country nested within date.

  • Two-level model: the units of analysis (Level 1), countries, are nested within clusters (Level 2), date;

  • The variability of the data comes from nested sources;

  • The Intraclass Correlation Coefficient (ICC) is equal to \(0.3910876\) for date, equals \(0.04668614\) for id and $ 0.02533497$ for Clusters.

lot to understand the variability respect date

and respect Clusters:

and id:

How to choose the random and fixed part?

The problem is much more complicated than in linear regression because selection on the covariance structure is not straightforward due to computational issues and boundary problems arising from positive semidefinite constraints on covariance matrices.

-Conditional AIC (Package cAIC4): The conditional AIC is also appropriate for choosing between a simple null model without any random effects and a complex model incorporating random effects,

-Boostrap (R Package pbkrtest): Model comparison of nested models using parametric bootstrap methods. Implemented for some commonly applied model types.

Finally the model is:

FALSE  Family: nbinom2  ( log )
FALSE Formula:          
FALSE active_lag ~ pca_EC + pop_density_log + surface_area_log + pca_hs +  
FALSE     workplace_closingF + gatherings_restrictionsF + transport_closingF +  
FALSE     stay_home_restrictionsF + testing_policyF + contact_tracingF +  
FALSE     Clusters + (0 + pca_LD | id) + (1 | date2) + (1 | Clusters)
FALSE Data: dat
FALSE  Offset: log(active + 1)
FALSE 
FALSE      AIC      BIC   logLik deviance df.resid 
FALSE  40748.6  40921.6 -20344.3  40688.6     2330 
FALSE 
FALSE Random effects:
FALSE 
FALSE Conditional model:
FALSE  Groups   Name        Variance  Std.Dev. 
FALSE  id       pca_LD      2.928e-01 5.411e-01
FALSE  date2    (Intercept) 4.169e+00 2.042e+00
FALSE  Clusters (Intercept) 4.215e-09 6.492e-05
FALSE Number of obs: 2360, groups:  id, 20; date2, 158; Clusters, 5
FALSE 
FALSE Overdispersion parameter for nbinom2 family (): 1.07 
FALSE 
FALSE Conditional model:
FALSE                           Estimate Std. Error z value Pr(>|z|)    
FALSE (Intercept)               -0.95466    0.70894  -1.347  0.17811    
FALSE pca_EC                    -0.53735    0.07044  -7.629 2.37e-14 ***
FALSE pop_density_log            0.15443    0.04620   3.342  0.00083 ***
FALSE surface_area_log           0.05360    0.03587   1.494  0.13510    
FALSE pca_hs                     0.05193    0.02029   2.559  0.01050 *  
FALSE workplace_closingF1       -0.24604    0.14061  -1.750  0.08016 .  
FALSE workplace_closingF2       -1.12441    0.14061  -7.997 1.28e-15 ***
FALSE workplace_closingF3       -0.46986    0.17228  -2.727  0.00638 ** 
FALSE gatherings_restrictionsF1 -0.52789    0.16317  -3.235  0.00122 ** 
FALSE gatherings_restrictionsF2 -1.22558    0.14231  -8.612  < 2e-16 ***
FALSE gatherings_restrictionsF3 -1.48631    0.17392  -8.546  < 2e-16 ***
FALSE gatherings_restrictionsF4 -1.67393    0.17987  -9.306  < 2e-16 ***
FALSE transport_closingF1       -0.04257    0.10635  -0.400  0.68897    
FALSE transport_closingF2       -0.44643    0.20266  -2.203  0.02761 *  
FALSE stay_home_restrictionsF1  -0.06059    0.10879  -0.557  0.57758    
FALSE stay_home_restrictionsF2  -0.13755    0.14964  -0.919  0.35799    
FALSE stay_home_restrictionsF3  -0.87098    0.29387  -2.964  0.00304 ** 
FALSE testing_policyF1           0.20317    0.09147   2.221  0.02633 *  
FALSE testing_policyF2           0.55401    0.11289   4.908 9.21e-07 ***
FALSE testing_policyF3           1.30708    0.16002   8.168 3.13e-16 ***
FALSE contact_tracingF1          0.20257    0.08292   2.443  0.01456 *  
FALSE contact_tracingF2          0.37629    0.09576   3.929 8.51e-05 ***
FALSE ClustersCl2                1.47291    0.17353   8.488  < 2e-16 ***
FALSE ClustersCl3                1.93534    0.15847  12.213  < 2e-16 ***
FALSE ClustersCl4                2.34541    0.14849  15.795  < 2e-16 ***
FALSE ClustersCl5                2.43211    0.16041  15.162  < 2e-16 ***
FALSE ---
FALSE Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

5 Italian lockdown and regional outcomes

6 Effect of policies from a global perspective

7 Supplementary materials

All the codes used for this analysis is available on Github.

Dong, E., H. Du, and L. Gardner. 2020. “An Interactive Web-Based Dashboard to Track Covid-19 in Real Time.” Lancet Infect Dis.

Thomas, H., S. Webster, A. Petherick, T. Phillips, and B. Kira. 2020. “Oxford Covid-19 Government Response Tracker, Blavatnik School of Government.” Data Use Policy: Creative Commons Attribution CC BY Standard.